David Blaschke (Univ. Wroclaw & JINR Dubna)

Transcription

1 David Blaschke (Univ. Wroclaw & JINR Dubna) INT Workshop, Seattle, August 15 th, 28

2 David Blaschke (Univ. Wroclaw & JINR Dubna) NCQM as a tool for strong QCD T,µ Mean-field: order params. & phase diagram Flucuations: mesons & Mott effect Gibbs constr: compact stars vs. CBM et al. INT Workshop, Seattle, August 15 th, 28

3 3. 2SC DBHF Hybrid 4. d-csl DBHF hybrid Partition function for chiral Quark Field theory { β Z[T, V, µ] = D ψdψ exp dτ V d 3 x[ ψ(iγ µ µ m γ µ)ψ L int ] Current-current coupling (4-fermion interaction) L int = M=π,σ,... G M( ψγ M ψ) 2 D G D( ψ C Γ D ψ) 2 Bosonisation (Hubbard-Stratonovich Transformation) { Z[T, V, µ] = Dφ M D D D D exp φ 2 M 4G M M D Collective (stochastic) Fields: Mesons (φ M ) and Diquarks ( D ) Systematic Evaluation: Mean field Fluctuations } } D 2 1 4G D 2 Tr lns 1 [{M M }, { D }] Mean-field Approximation: Order parameter for Phase transitions (Gap equations) Fluctuations (2. Order): Hadronic Correlations (Bound- & Scattering states) Fluctuations of higher Order: Hadron-Hadron Interaction

4 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling 5. Summary Euclidean action at T, µ = { S E = d 4 x ψ(x) ( i/ m) ψ(x) G M 2 jf M (x)jf M (x) G } D 2 [ja D(x)] jd(x) a Two alternatives to introduce nonlocality Model I Instanton Liquid Model inspired j f M (x) = j a D(x) = d 4 y d 4 z r(y x) r(x z) ψ(y) Γ f ψ(z), d 4 y d 4 z r(y x) r(x z) ψ C (y) iγ 5 τ 2 λ a ψ(z) Model II One-Gluon- Exchange inspired j f M (x) = j a D(x) = d 4 z g(z) ψ(x z 2 ) Γ f ψ(x z 2 ), d 4 z g(z) ψ C (x z 2 ) iγ 5τ 2 λ a ψ(x z 2 ) r(x y) and g(z) are nonlocal regulators, ψ C (x) = γ 2 γ 4 ψt (x), Γ f = (1, iγ 5 τ) Gomez-Dumm, D.B., Grunfeld, Scoccola, arxiv:hep-ph/512218; Phys. Rev. D 73 (26).

5 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling s Map of Armenia: Three phases of quark matter: confined, deconfined, superconducting Ararat

6 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling s Armenia in Europe: Three phases of quark matter: confined, deconfined, superconducting Ararat T [MeV] % 5% 8% Crossover Critical endpoint 1 st order Confinement phase,1,2,3,4,5 µ [GeV] transitions T 2sc T χ Normal quark matter phase 2 nd order transitions 2SC phase

7 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling s Map of routes: Route 1: deconfined confined T [MeV] 15 2% 8% 1 5 5% Crossover Critical endpoint 1 st order Confinement phase 2SC phase,1,2,3,4,5 µ [GeV] The Olgas transitions T 2sc T χ Normal quark matter phase 2 nd order transitions

8 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling s Map of routes: Route 1 : deconfined confined T [MeV] 15 2% 8% 1 5 5% Crossover Critical endpoint 1 st order Confinement phase 2SC phase,1,2,3,4,5 µ [GeV] Mount Rainier transitions T 2sc T χ Normal quark matter phase 2 nd order transitions

9 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling s Map of routes: Route 2: confined superconducting T [MeV] 15 2% 8% 1 5 5% Crossover Critical endpoint 1 st order Confinement phase 2SC phase,1,2,3,4,5 µ [GeV] Schneekoppe transitions T 2sc T χ Normal quark matter phase 2 nd order transitions

10 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling s Map of routes: Route 3: deconfined superconducting T [MeV] 15 2% 8% 1 5 5% Crossover Critical endpoint 1 st order Confinement phase 2SC phase,1,2,3,4,5 µ [GeV] Mount Everest transitions T 2sc T χ Normal quark matter phase 2 nd order transitions

11 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling 5. Summary Instanton model (left) vs. One-Gluon-Exchange model (right) H =.5 G H =.5 G T [ MeV ] CSB NQM 2SC EP NQM 4 2 EP g2sc CSB T [ MeV ] CSB H =.75 G EP 3P NQM g2sc 2SC Mixed EP CSB H =.75 G 3P NQM 2SC g2sc Mixed T [ MeV ] CSB H = G NQM 3P 2SC g2sc CSB EP 3P H = G NQM g2sc 2SC µ [ MeV ] µ [ MeV ]

12 3. 2SC DBHF hybrid 4. d-csl hybrid p (GeV) BHAGWAT, PICHOWSKY, ROBERTS, TANDY, PHYS. REV. C68 (23) 1523 S(p) 1 = i/pa(p 2 ) B(p 2 ), M(p 2 ) = B(p 2 )/A(p 2 ) Z(p 2 ) = 1/A(p 2 ) S(p) sum of N pairs of complex conj. mass poles N { 1 zi z } i S(p) = Z 2 i/p m i i/p m = i/pσ V (p 2 ) σ S (p 2 ) i i=1 Representation of the scalar amplitude N { } σ S (p 2 ) = Z2 1 zi m i p 2 m 2 z i m i i p 2 m i 2 i=1 Derivation of the equivalent separable model (in Feynman-like gauge) D µν (p q) = δ µν D(p, q) and D(p, q) = f (p 2 ) f (q 2 ) f 1 (p 2 ) p q f 1 (q 2 ) f 1 (p 2 ) = A(p2 ) 1 ; f (p 2 ) = B(p2 ) m c a b b 2 = 16 3 a 2 = 8 3 Λ q Λ q [B(q 2 ) m c ]σ s (q 2 ) [A(q 2 ) 1] q2 4 σ v(q 2 )

13 3. 2SC DBHF hybrid 4. d-csl hybrid nq /T 3 Ψ Ψ Ψ Ψ T T GeV µ=.6 Tc T/T c Grand canonical thermodynamical potential Ω(T, µ; Φ, m) = σ2 d 3 2G 6N p f (2π) 3E p θ ( Λ 2 p 2) d 3 p { 2N f T (2π) 3 Trc ln [1 ] L e (E p µ)/t Tr c ln [1 ] L e (E p } ( ) µ)/t U Φ, Φ, T Appearance of quarks below T c largely suppressed: [ ] ln det 1 L e (E p µ)/t ln det [1 ] L e (E p µ)/t [ = ln 1 3 (Φ Φe ) ] (E p µ)/t e (E p µ)/t e 3 (E p µ)/t [ ln 1 3 ( Φ ) ] Φe (E p µ)/t e (E p µ)/t e 3 (E p µ)/t. Accordance with QCD lattice susceptibilities! Example: n q (T, µ) = 1 Ω (T, µ), T 3 T 3 µ Ratti, Thaler, Weise, PRD 73 (26) 1419.

14 3. 2SC DBHF hybrid 4. d-csl hybrid rank-1 separable, two-flavor, Instanton model rank-2 separable, three-flavor, OGE model 1 w Polyakov loop w/o Polyakov loop m d / m d vac and Φ susceptibilities N f =21 dφ(τ)/dt dm u,d (T)/dT dm s (T)/dT N f = T, GeV D.B., Buballa, Radzhabov, Volkov, arxiv: Yad. Fiz. (28) in press temperature T[GeV] temperature T[GeV] D.B., Horvatic, Klabucar, Radzhabov, in prep.

15 3. 2SC DBHF hybrid 4. d-csl hybrid [ Ω(T ) = = U(Φ, Φ) T Tr p,n,α,f,d ln{s 1 f (pα n, T )} 1 ] 2 Σ f(p α n, T ) S f (p α n, T ), (1) where the full quark propagator for the flavor f = u, d, s, S 1 f (pα n, T ) = S 1 f, (pα n, T ) Σ 1 f (pα n, T ) = i γ p A f ((p α n) 2, T ) iγ 4 ω n C f ((p α n) 2, T ) B f ((p α n) 2, T ), (2) is defined by the DSE for the quark selfenergy Σ, see below. The Polyakov-loop potential is of the form: U(Φ, Φ) T 4 = 1 2 a(t )Φ Φ b(t ) ln [ 1 6Φ Φ 4(Φ 3 Φ 3 ) 3(Φ Φ) 2]. (3) The Matsubara 4-momenta are defined as (p α n )2 = (ωn α)2 p 2, ωn α = ω n αφ 3, α = 1,, 1, and are coupled to the Polyakov-loop variable Φ = Φ ( ) ( )) = 1 N c 1 e iφ 3 T e iφ 3 T = 1 N c (1 2 cos φ3. via the parameter φ T 3. Employing for the effective gluon propagator in a Feynman-like gauge, g 2 D eff µν (p q) = δ µν D(p 2, q 2, p q), a rank-2 separable ansatz D(p 2, q 2, p q) = D F (p 2 )F (q 2 ) D 1 F 1 (p 2 )(p q)f 1 (q 2 ), (4) the propagator amplitudes are given by B f (p 2 n, T ) = m f b f (T )F (p 2 n), (5) A f (p 2 n, T ) = 1 a f(t )F 1 (p 2 n ), (6) C f (p 2 n, T ) = 1 c f (T )F 1 (p 2 n), (7)

16 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling 5. Summary Thermodynamic Potential Ω(T, µ) = T ln Z[T, µ] Ω(T, µ) = φ2 u φ2 d φ2 s 8G S ud 2 us 2 ds 2 4G D T n d 3 p 1 Tr ln (2π) 3 2 ( ) 1 T S 1 (iω n, p) Ω e Ω. InverseNambu GorkovPropagator S 1 (iω n, p) = [ γ µ p µ M( p) µγ ( p) ( p) γ µ p µ M( p) µγ ], kγ = 2G D q iα iγ 5 ɛ αβγ ɛ ijk g( q)q C jβ. ( p) = iγ5 ɛ αβγ ɛ ijk kγ g( p). Fermion Determinant (Tr ln D = ln det D) ( ) 1 lndet T S 1 (iω n, p) = 2 18 Result for the thermodynamic Potential (Meanfield approximation) Ω(T, µ) = φ2 u φ 2 d φ2 s ud 2 us 2 ds 2 d 3 p 8G S 4G D (2π) 3 Neutrality constraints: n Q = n 8 = n 3 =, n i = Ω/ µ i =, Equations of state: P = Ω, etc. a=1 ( ω 2 ln n λ a ( p) 2 ). T 2 18 a=1 [ ( )] λ a 2T ln 1 e λ a/t Ω e Ω.

17 1. Introduction 2. Hadronic Cooling 3. Quark Substructure and Phases 4. Hybrid Star Cooling s, M [MeV] M s M u M d M u, M d ud us, ds E [MeV] ur-dg-sb ub-sr, db-sg ug-dr, ur-dg-sb ug-dr ub-sr db-sg (gapless) µ [MeV] 2 4 P [MeV] P [MeV] Dynamical quark masses and diquark gaps at T = for intermediate diquark coupling G D =.75 G S Dispersion relations for G D =.75 G S, T =, µ = 465 MeV (left), G D = 1. G S, T = 59 MeV, µ = 5 MeV (right) Rüster et al, PRD 72 (25) 344; Blaschke et al, PRD 72 (25) 652

18 3. 2SC DBHF hybrid 4. d-csl hybrid T [MeV] NQ χ 2SC =1 NQ-2SC g2sc 2SC gusc gcfl usc 2 CFL M s =175 MeV µ [MeV] Rüster et al, PRD 72 (25) 344; Blaschke et al, PRD 72 (25) 652; Abuki, Kunihiro, NPA768 (26) 118; Warringa et al, PRD 72 (25) 1415 The phases are: NQ: ud = us = ds = ; NQ-2SC: ud, us = ds =, χ 2SC 1; 2SC: ud, us = ds = ; usc: ud, us, ds = ; CFL: ud, ds, us ; Result: Gapless phases only at high T, CFL only at high chemical potential, At T 25-3 MeV: mixed NQ-2SC phase, Critical point (T c,µ c )=(48 MeV, 353 MeV), Strong coupling, G D = G S, similar, no NQ-2SC mixed phase.

19 3. 2SC DBHF hybrid 4. d-csl hybrid M [M sun ] causality constraint 4U U DBHF (Bonn A) η D =.92, η V =. η D = 1., η V =.5 η D = 1.2, η V =.5 η D = 1.3, η V =.5 η D = 1., η V =..7 XTE J RX J EXO z =.1 P [MeV fm -3 ] Flow constraint DBHF η D =.92, η V =. η D = 1., η V =.25 η D = 1.2, η V =.25 η D = 1.3, η V = R [km] n [fm -3 ].8 1 Large Mass ( 2 M ) and radius (R 12 km) stiff quark matter EoS; Note: DU problem of DBHF removed by deconfinement! and: CFL core Hybrids unstable! Flow in Heavy-Ion Collisions not too stiff EoS! Note: Quark matter removes violation by DBHF at high densities Klähn, D.B., Sandin, Fuchs, Faessler, Grigorian, Röpke, Trümper, Phys. Lett. B567, 16 (27)

20 3. 2SC DBHF hybrid 4. d-csl hybrid η D =.92 η V =. T [MeV] NM (DD-F4) 2SC η D = 1.3 η V =.25 η D =.933 η V =. η D =.75 η V =. CFL T [MeV] 5 NM (DDF4) 2SC CFL n B [fm -3 ] n B [fm -3 ] Phase diagrams for isospin-symmetric matter, for hybrid star maximum mass M max = 2.1 M (left-hand side) and M max = 1.7 M (right-hand side). D. B., F. Sandin, S. Typel, in preparation.

21 3. 2SC DBHF hybrid 4. d-csl hybrid T [ MeV ] χsb First order transition Second order transition Smooth crossover EP NQM [ MeV ] T = T = 5 MeV T = 1 MeV 5 χsb - 2SC 2SC µ [ MeV ] µ [ MeV ] Effect of the color neutrality constraint on the Polyakov-loop NJL phase diagram: Coexistence of χsb and 2SC phase = BEC-BCS crossover in the hadronic freezout region! D. Gomez-Dumm, D. B., G.A. Grunfeld, N.N. Scoccola, arxiv: [hep-ph]

22 free quarks bound quarks (nucleons) µd µu µd µu µd µu µe µc µe µe pure nuclear matter (NM) d quark drip (NM d CSL phase) 2 flavor quark matter (2SC phase) D.B., F. Sandin, T. Kla hn, J. Berdermann, arxiv: [nucl-th] Sequential deconfinement of quark flavors Mass and Flow constraint Chiral Quark model 2SC DBHF hybrid d-csl hybrid Conclusion

23 3. 2SC DBHF hybrid 4. d-csl hybrid µ d µ u µ s µ d µ u µ s µ d µ u µ s µ d µ u µ s µ e M u M d M s dd ud us, ds m d m u µ e m s µ e µ e, M [MeV] 1 1 CSL 2SC CFL 1 pure nuclear matter (NM) d quark drip (NM d CSL phase) 2 flavor quark matter (2SC phase) 3 flavor quark matter (CFL phase) D.B., F. Sandin, T. Klähn, J. Berdermann, 1 arxiv: [nucl-th] µ B [MeV], M [MeV] 1 1 CSL 2SC CSL 2SC CFL

24 3. 2SC DBHF hybrid 4. d-csl hybrid Ansatz: isotropic Color-spin-locking (CSL) ˆ = (γ 3 λ 2 γ 1 λ 7 γ 2 λ 5 ) E i [MeV] i = 1 i = 3 i = 5 M = 33 MeV p [MeV] M = 4 MeV p [MeV] Μ (p=) [MeV] [MeV] M = 33 MeV µ [MeV] NJL L1 L5 L3 M = 4 MeV µ [MeV] See also: Schmitt, Wang, Rischke, PRD 66, 1141 (22) Aguilera et al., PRD 72 (25) 348; PRD 74 (26) 1145

25 3. 2SC DBHF hybrid 4. d-csl hybrid Dash-dotted lines: border between oppositely charged phases -1 DBHF 2SC -1 Shen 2SC µ Q [MeV] µ Q [MeV] -2 d-csl NQ -2 d-csl NQ -3 nd = 13 n u µ B [MeV] -3 nd = 13 n u µ B [MeV] D.B., F. Sandin, T. Klähn, J. Berdermann, in preparation.

26 3. 2SC DBHF hybrid 4. d-csl hybrid Equation of state Configuration Sequences P [MeV/fm 3 ] Nuclear-CSL DBHF-NJL, η D =.75 Shen-NJL, η D =.75 2SC-NQ 2SC-CSL n B [fm -3 ] CFL M [M sun ] causality 4U 1636 RXJ R [km] ShenCSL DBHFCSL 2SCCSL 2SCNQ 2SCNQ CFL CFL Nuclear (DBHF) Hybrid (DBHF QM) Hybrid (Shen QM) n B (r=) [fm -3 ] D. B., F. Sandin, T. Klähn, J. Berdermann, arxiv: [nucl-th]

27 3. 2SC DBHF hybrid 4. d-csl hybrid d-quark drip at crust-core boundary: Candidate for deep crustal heating (DCH) process? 1 Total density Nuclear matter d-csl phase Haensel and Zdunik,A& A 227, 431 (199) Ushomirsky and Rutledge, MNRAS 325, 1157 (21) Page and Cumming,ApJ 635, L157 (25): Superbursts & Strange Stars Stejner and Madsen,A& A 458, 523 (26): SS Transient Cooling Shternin, Yakovlev, Haensel and Potekhin, MNRAS 382, L43 (27): KS1731 n B [fm -3 ].1 M = 1.4 M sun M = 2. M sun m B - dm/dn [MeV] 2 1 DBHF DBHFCSL 1 MeV 7 MeV r [km] r [km] D. B., F. Sandin, T. Klähn, J. Berdermann, arxiv: [nucl-th] 1 2 N [N sun ]

28 3. 2SC DBHF hybrid 4. d-csl hybrid Cooling: processes in single-flavor quark matter are blocked! log(t s [K]) PSR J2564 in 3C58 d-csl phase: Quark processes are excluded Cooling for HJ EoS (AV18) Our crust, with medium effects, 3P 2 *.1 Crab RX J Crust: Tsuruta law; Gaps: AV18 1E RX J log(t[yr]) Vela CTA 1 D. B., F. Sandin, H. Grigorian, in preparation. M/M sun = PSR Geminga PSR RX J Quark Urca - d ν e- Momentum conservation triangle du p F,u p F,d ue de u p F,e not operative since u-quark Fermi sea not populated (p F,u = )

29 Constraints on the high-density EoS Compact star masses 2 M require stiff EoS Flow data provide upper limits on the stiffness Local charge neutrality: 2SC DBHF hybrid diquark coupling lowers phase transition density vector meanfield stiffens quark matter EoS Global charge neutrality: d-csl DBHF hybrid single flavor phase (d-csl) as consequence of dynamical χsr no d-csl in symmetric matter: x p,crit <.2 no Urca cooling processes no neutrino trapping? apply to superbursts, X-ray transients, high-mass supernovae extend to inhomogeneous phases: surface tension and Coulomb effects